DESCRIPTION (Applicant's abstract): Epidemiology plays a major role in the identification of carcinogenic agents and in the quantification of dose time response relationships upon which regulation and preventive strategies are based. Epidemiology as a science depends critically upon statistics. The goal of this project is the development of more efficient statistical designs and methods of analysis for both analytic and descriptive studies. There are two major areas of emphasis. First, many studies involve the estimation of a large number of related quantities, such as multiple disease rates in small areas for identification of "hot spots" and construction of disease incidence maps. Evaluation of community based intervention programs and meta-analyses of data from multiple studies likewise require consideration of "random effects" to represent unexplained heterogeneity at the level of the community or the study. A major goal is the development, evaluation and implementation of hierarchical statistical models that allow for the efficient estimation of both random and fixed effects in such settings. Second, two-phase case- control studies, exposure stratified case-cohort studies and other complex stratified designs are of great value in limiting the collection of costly data to those subjects who are most informative regarding disease/risk factor associations. An important example is the validation substudy conducted to alleviate the effects of measurement error. Here "gold standard" measurements are made for a small number of subjects in a random subsample. More efficient methods of study design will be developed based on stratification of the validation sample using measurements available for all subjects. More efficient methods of statistical analysis will be developed using the tools of modem semiparametric inference. Such designs and efficient new analysis methods can dramatically reduce study costs while yielding estimates that are almost as good as when "gold standard" measurements are made for everyone. The methods used to achieve these goals include mathematical and statistical analysis, computer simulation and application to important datasets collected by cancer epidemiologists and other public health scientists.